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A geometric model for the module category of a string algebra

Research output: Working paperPreprint

Unpublished
Publication date12/03/2024
PublisherArxiv
Number of pages33
<mark>Original language</mark>English

Abstract

In this paper, we give a geometric construction of string algebras and of their module categories. Our approach uses dissections of punctured Riemann surfaces with extra data at marked points, called labels. As an application, we give a classification of support tau-tilting modules in terms of arcs in such a tiled surface. In the case when the string algebra is gentle, we recover the classification given arXiv:2004.11136.